Problem: Simplify the following expression: $\dfrac{50n^2}{40n^2}$ You can assume $n \neq 0$.
Answer: $ \dfrac{50n^2}{40n^2} = \dfrac{50}{40} \cdot \dfrac{n^2}{n^2} $ To simplify $\frac{50}{40}$ , find the greatest common factor (GCD) of $50$ and $40$ $50 = 2 \cdot 5 \cdot 5$ $40 = 2 \cdot 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(50, 40) = 2 \cdot 5 = 10 $ $ \dfrac{50}{40} \cdot \dfrac{n^2}{n^2} = \dfrac{10 \cdot 5}{10 \cdot 4} \cdot \dfrac{n^2}{n^2} $ $\phantom{ \dfrac{50}{40} \cdot \dfrac{2}{2}} = \dfrac{5}{4} \cdot \dfrac{n^2}{n^2} $ $ \dfrac{n^2}{n^2} = \dfrac{n \cdot n}{n \cdot n} = 1 $ $ \dfrac{5}{4} \cdot 1 = \dfrac{5}{4} $